We present a two-step method specifically tailored for band structure calculation of the small-angle moir\'{e}-pattern materials which contain tens thousands atoms in unit cell. In first step, self-consistent field ground state is performed with $O(N)$ Krylov subspace implemented OpenMX. Secondly, crystal momentum dependent Bloch Hamiltonian and overlap matrix are constructed from results obtai...

this study develops and analyzes preconditioned krylov subspace methods to solve linear systemsarising from discretization of the time-independent space-fractional models. first, we apply shifted grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. then, we employee two preconditioned iterative methods, namely, the preconditioned gene...

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...

We consider the Radon transform for a dual pair $(X,\Xi)$, where $X=G/K$ is noncompact symmetric space and $\Xi$ of horocycles $X$. address unitarization problem that was considered (and solved in some cases) by Helgason, namely determination pseudo-differential operator such pre-composition with extends to unitary $\mathcal{Q}\colon L^2(X)\to L_\flat^2(\Xi)$, $L_\flat^2(\Xi)$ closed subspace $...

this article presents a new subspace-based technique for reducing the noise ofsignals in time-series. in the proposed approach, the signal is initially representedas a data matrix. then using singular value decomposition (svd), noisy datamatrix is divided into signal subspace and noise subspace. in this subspace division,each derivative of the singular values with respect to rank order is used ...

in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...

Presentations \\ a la Coxeter" are given for all (irreducible) nite complex reeec-tion groups. They provide presentations for the corresponding generalized braid groups (still conjectural in some cases) which allow us to generalize some of the known properties of nite Coxeter groups (center of the braid group, construction of Hecke algebras). 1. Background from complex reflection groups For all...